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International Symposium on Algorithms and Computation

ISAAC 1993: Algorithms and Computation pp 176–184Cite as

On quadratic lattice approximations

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 762))

Abstract

We consider the problem of approximating a system of linear and quadratic forms evaluated at a rational point by 0–1 vectors. When only linear forms are given this is the well known lattice approximation problem. We call the general version the quadratic lattice approximation problem. In this paper we construct via derandomization lattice points with small linear and quadratic discrepancies. Unfortunately the known derandomization methods do not apply to the quadratic variant of the lattice approximation problem. Therefore we develop a new derandomization technique, which captures non-linearity and dependencies among the random variables under consideration, extending the conditional probability/pessimistic estimator method of Spencer and Raghavan. The essential new tool is an algorithmic version of Azuma's martingale inequality.

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Author information

Authors and Affiliations

  1. Research Institute of Discrete Mathematics, University of Bonn, Germany

    Anand Srivastav

  2. Institute for Computer Science, University of Cologne, Germany

    Peter Stangier

Authors
  1. Anand Srivastav
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  2. Peter Stangier
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Editor information

K. W. Ng P. Raghavan N. V. Balasubramanian F. Y. L. Chin

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© 1993 Springer-Verlag Berlin Heidelberg

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Srivastav, A., Stangier, P. (1993). On quadratic lattice approximations. In: Ng, K.W., Raghavan, P., Balasubramanian, N.V., Chin, F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57568-5_247

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  • DOI: https://doi.org/10.1007/3-540-57568-5_247

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57568-9

  • Online ISBN: 978-3-540-48233-8

  • eBook Packages: Springer Book Archive

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